Siam-Asa Journal on Uncertainty Quantification最新文献

The Bayesian Approach to Inverse Robin Problems 逆向罗宾问题的贝叶斯方法

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-09-11 DOI: 10.1137/23m1620624

Aksel K. Rasmussen, Fanny Seizilles, Mark Girolami, Ieva Kazlauskaite

{"title":"The Bayesian Approach to Inverse Robin Problems","authors":"Aksel K. Rasmussen, Fanny Seizilles, Mark Girolami, Ieva Kazlauskaite","doi":"10.1137/23m1620624","DOIUrl":"https://doi.org/10.1137/23m1620624","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 3, Page 1050-1084, September 2024. Abstract.In this paper, we investigate the Bayesian approach to inverse Robin problems. These are problems for certain elliptic boundary value problems of determining a Robin coefficient on a hidden part of the boundary from Cauchy data on the observable part. Such a nonlinear inverse problem arises naturally in the initialization of large-scale ice sheet models that are crucial in climate and sea-level predictions. We motivate the Bayesian approach for a prototypical Robin inverse problem by showing that the posterior mean converges in probability to the data-generating ground truth as the number of observations increases. Related to the stability theory for inverse Robin problems, we establish a logarithmic convergence rate for Sobolev-regular Robin coefficients, whereas for analytic coefficients we can attain an algebraic rate. The use of rescaled analytic Gaussian priors in posterior consistency for nonlinear inverse problems is new and may be of separate interest in other inverse problems. Our numerical results illustrate the convergence property in two observation settings.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Covariance Expressions for Multifidelity Sampling with Multioutput, Multistatistic Estimators: Application to Approximate Control Variates 使用多输出、多统计估计器进行多保真度采样的协方差表达式：近似控制变量的应用

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-09-09 DOI: 10.1137/23m1607994

Thomas O. Dixon, James E. Warner, Geoffrey F. Bomarito, Alex A. Gorodetsky

{"title":"Covariance Expressions for Multifidelity Sampling with Multioutput, Multistatistic Estimators: Application to Approximate Control Variates","authors":"Thomas O. Dixon, James E. Warner, Geoffrey F. Bomarito, Alex A. Gorodetsky","doi":"10.1137/23m1607994","DOIUrl":"https://doi.org/10.1137/23m1607994","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 3, Page 1005-1049, September 2024. Abstract.We provide a collection of results on covariance expressions between Monte Carlo–based multioutput mean, variance, and Sobol main effect variance estimators from an ensemble of models. These covariances can be used within multifidelity uncertainty quantification strategies that seek to reduce the estimator variance of high-fidelity Monte Carlo estimators with an ensemble of low-fidelity models. Such covariance expressions are required within approaches such as the approximate control variate and multilevel best linear unbiased estimator. While the literature provides these expressions for some single-output cases such as mean and variance, our results are relevant to both multiple function outputs and multiple statistics across any sampling strategy. Following the description of these results, we use them within an approximate control variate scheme to show that leveraging multiple outputs can dramatically reduce estimator variance compared to single-output approaches. Synthetic examples are used to highlight the effects of optimal sample allocation and pilot sample estimation. A flight-trajectory simulation of entry, descent, and landing is used to demonstrate multioutput estimation in practical applications.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142213297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Parameter Inference Based on Gaussian Processes Informed by Nonlinear Partial Differential Equations 基于非线性偏微分方程的高斯过程的参数推理

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-08-30 DOI: 10.1137/22m1514131

Zhaohui Li, Shihao Yang, C. F. Jeff Wu

{"title":"Parameter Inference Based on Gaussian Processes Informed by Nonlinear Partial Differential Equations","authors":"Zhaohui Li, Shihao Yang, C. F. Jeff Wu","doi":"10.1137/22m1514131","DOIUrl":"https://doi.org/10.1137/22m1514131","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 3, Page 964-1004, September 2024. Abstract.Partial differential equations (PDEs) are widely used for the description of physical and engineering phenomena. Some key parameters involved in PDEs, which represent certain physical properties with important scientific interpretations, are difficult or even impossible to measure directly. Estimating these parameters from noisy and sparse experimental data of related physical quantities is an important task. Many methods for PDE parameter inference involve a large number of evaluations for numerical solutions to PDEs through algorithms such as the finite element method, which can be time consuming, especially for nonlinear PDEs. In this paper, we propose a novel method for the inference of unknown parameters in PDEs, called the PDE-informed Gaussian process (PIGP)–based parameter inference method. Through modeling the PDE solution as a Gaussian process (GP), we derive the manifold constraints induced by the (linear) PDE structure such that, under the constraints, the GP satisfies the PDE. For nonlinear PDEs, we propose an augmentation method that transforms the nonlinear PDE into an equivalent PDE system linear in all derivatives, which our PIGP-based method can handle. The proposed method can be applied to a broad spectrum of nonlinear PDEs. The PIGP-based method can be applied to multidimensional PDE systems and PDE systems with unobserved components. Like conventional Bayesian approaches, the method can provide uncertainty quantification for both the unknown parameters and the PDE solution. The PIGP-based method also completely bypasses the numerical solver for PDEs. The proposed method is demonstrated through several application examples from different areas.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142213379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Adaptive Multilevel Subset Simulation with Selective Refinement 具有选择性细化功能的自适应多级子集模拟

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-08-23 DOI: 10.1137/22m1515240

D. Elfverson, R. Scheichl, S. Weissmann, F. A. Diaz De La O

{"title":"Adaptive Multilevel Subset Simulation with Selective Refinement","authors":"D. Elfverson, R. Scheichl, S. Weissmann, F. A. Diaz De La O","doi":"10.1137/22m1515240","DOIUrl":"https://doi.org/10.1137/22m1515240","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 3, Page 932-963, September 2024. Abstract. In this work we propose an adaptive multilevel version of subset simulation to estimate the probability of rare events for complex physical systems. Given a sequence of nested failure domains of increasing size, the rare event probability is expressed as a product of conditional probabilities. The proposed new estimator uses different model resolutions and varying numbers of samples across the hierarchy of nested failure sets. In order to dramatically reduce the computational cost, we construct the intermediate failure sets such that only a small number of expensive high-resolution model evaluations are needed, whilst the majority of samples can be taken from inexpensive low-resolution simulations. A key idea in our new estimator is the use of a posteriori error estimators combined with a selective mesh refinement strategy to guarantee the critical subset property that may be violated when changing model resolution from one failure set to the next. The efficiency gains and the statistical properties of the estimator are investigated both theoretically via shaking transformations, as well as numerically. On a model problem from subsurface flow, the new multilevel estimator achieves gains of more than a factor 60 over standard subset simulation for a practically relevant relative error of 25%.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142213380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Fully Parallelized and Budgeted Multilevel Monte Carlo Method and the Application to Acoustic Waves 完全并行化和预算多级蒙特卡洛方法及其在声波中的应用

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-08-19 DOI: 10.1137/23m1588354

Niklas Baumgarten, Sebastian Krumscheid, Christian Wieners

引用次数: 0

Conditional Sampling with Monotone GANs: From Generative Models to Likelihood-Free Inference 单调 GAN 的条件采样：从生成模型到无似然推理

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-08-09 DOI: 10.1137/23m1581546

Ricardo Baptista, Bamdad Hosseini, Nikola B. Kovachki, Youssef M. Marzouk

引用次数: 0

Harmonizable Nonstationary Processes 可协调的非稳态过程

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-07-30 DOI: 10.1137/22m1544580

Mircea Grigoriu

引用次数: 0

Spectral Convergence of a Semi-discretized Numerical System for the Spatially Homogeneous Boltzmann Equation with Uncertainties 具有不确定性的空间均质玻尔兹曼方程半离散数值系统的谱收敛性

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-07-24 DOI: 10.1137/24m1638483

Liu Liu, Kunlun Qi

引用次数: 0

Emulating Complex Dynamical Simulators with Random Fourier Features 用随机傅立叶特征模拟复杂动态模拟器

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-07-22 DOI: 10.1137/22m147339x

Hossein Mohammadi, Peter Challenor, Marc Goodfellow

{"title":"Emulating Complex Dynamical Simulators with Random Fourier Features","authors":"Hossein Mohammadi, Peter Challenor, Marc Goodfellow","doi":"10.1137/22m147339x","DOIUrl":"https://doi.org/10.1137/22m147339x","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 3, Page 788-811, September 2024. Abstract.A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the numerical flow map of the system over an initial (short) time step, where the flow map is a function that describes the evolution of the system from an initial condition to a subsequent value at the next time step. This yields a probabilistic distribution over the entire flow map function, with each draw offering an approximation to the flow map. The model output time series is then predicted (under the Markov assumption) by drawing a sample from the emulated flow map (i.e., its posterior distribution) and using it to iterate from the initial condition ahead in time. Repeating this procedure with multiple such draws creates a distribution over the time series. The mean and variance of this distribution at a specific time point serve as the model output prediction and the associated uncertainty, respectively. However, drawing a GP posterior sample that represents the underlying function across its entire domain is computationally infeasible, given the infinite-dimensional nature of this object. To overcome this limitation, one can generate such a sample in an approximate manner using random Fourier features (RFF). RFF is an efficient technique for approximating the kernel and generating GP samples, offering both computational efficiency and theoretical guarantees. The proposed method is applied to emulate several dynamic nonlinear simulators including the well-known Lorenz and van der Pol models. The results suggest that our approach has a promising predictive performance and the associated uncertainty can capture the dynamics of the system appropriately.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141739021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Hyperparameter Estimation for Sparse Bayesian Learning Models 稀疏贝叶斯学习模型的超参数估计

IF 2 3区工程技术

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-07-19 DOI: 10.1137/24m162844x

Feng Yu, Lixin Shen, Guohui Song

{"title":"Hyperparameter Estimation for Sparse Bayesian Learning Models","authors":"Feng Yu, Lixin Shen, Guohui Song","doi":"10.1137/24m162844x","DOIUrl":"https://doi.org/10.1137/24m162844x","url":null,"abstract":"SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 3, Page 759-787, September 2024. Abstract.Sparse Bayesian learning (SBL) models are extensively used in signal processing and machine learning for promoting sparsity through hierarchical priors. The hyperparameters in SBL models are crucial for the model’s performance, but they are often difficult to estimate due to the nonconvexity and the high-dimensionality of the associated objective function. This paper presents a comprehensive framework for hyperparameter estimation in SBL models, encompassing well-known algorithms such as the expectation-maximization, MacKay, and convex bounding algorithms. These algorithms are cohesively interpreted within an alternating minimization and linearization (AML) paradigm, distinguished by their unique linearized surrogate functions. Additionally, a novel algorithm within the AML framework is introduced, showing enhanced efficiency, especially under low signal noise ratios. This is further improved by a new alternating minimization and quadratic approximation paradigm, which includes a proximal regularization term. The paper substantiates these advancements with thorough convergence analysis and numerical experiments, demonstrating the algorithm’s effectiveness in various noise conditions and signal-to-noise ratios.","PeriodicalId":56064,"journal":{"name":"Siam-Asa Journal on Uncertainty Quantification","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141739022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0